Answer: [tex]17.7\ feet[/tex]
Step-by-step explanation:
Draw a right triangle as the one shown attached.
In order to calculate the distance from the base of the ladder to the house, you can use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.
Solving for one of the legs:
[tex]b=\sqrt{a^2-c^2}[/tex]
You can notice that:
[tex]a=19\ ft\\c=7\ ft\\b=x[/tex]
Therefore, substituting values into [tex]b=\sqrt{a^2-c^2}[/tex], you get that the distance from the base of the ladder to the house, rounded to the nearest tenth, is:
[tex]x=\sqrt{(19\ ft)^2-(7\ ft)^2}\\\\x=17.7\ ft[/tex]
